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Heat transfer characteristics of thin power-law liquid films over horizontal stretching sheet with internal heating and variable thermal coefficient

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Abstract

The effect of internal heating source on the film momentum and thermal transport characteristic of thin finite power-law liquids over an accelerating unsteady horizontal stretched interface is studied. Unlike most classical works in this field, a general surface temperature distribution of the liquid film and the generalized Fourier’s law for varying thermal conductivity are taken into consideration. Appropriate similarity transformations are used to convert the strongly nonlinear governing partial differential equations (PDEs) into a boundary value problem with a group of two-point ordinary differential equations (ODEs). The correspondence between the liquid film thickness and the unsteadiness parameter is derived with the BVP4C program in MATLAB. Numerical solutions to the self-similarity ODEs are obtained using the shooting technique combined with a Runge-Kutta iteration program and Newton’s scheme. The effects of the involved physical parameters on the fluid’s horizontal velocity and temperature distribution are presented and discussed.

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Abbreviations

a, b :

positive constant, s-1

C p :

specific heat capacity, J · kg-1 · K-1

d :

positive constant, m-r1

f :

dimensionless stream function

h :

liquid film thickness, m

K :

viscosity coefficient, kg · m-1 · sn-2

k :

effective thermal conductivity, W· m-1 · K-1

n :

power-law index

Pr :

generalized Prandtl number

Re x :

local Reynolds number

r 1 :

r 2, power indices

S :

unsteadiness parameter

S 0 :

critical value

T :

temperature, K

T 0 :

temperature at origin, K

T ref :

standard temperature, K

T s :

temperature of stretched surface, K

t :

time, s

u, v :

liquid velocity components along with x-direction and y-direction, respectively, m · s-1

u s :

horizontal velocity of stretched surface, m · s-1

x, y :

streamwise coordinate and cross-stream coordinate, respectively, m.

β :

dimensionless film thickness

η :

similarity variable

θ :

dimensionless temperature

ρ :

density, kg · m-3

τ xy :

modified shear viscous drag, N · m-2

φ :

heating source parameter

ψ :

stream function, m2 · s-1

ω :

consistency thermal coefficient, kg · m · sn-4 · K-1 s, for wall surface or stretched surface.

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Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, Fujian Province, China

    Yanhai Lin

  2. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China

    Liancun Zheng

  3. Department of Physics, Blinn College, Bryan, TX, 77805, USA

    Lianxi Ma

Authors
  1. Yanhai Lin
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  2. Liancun Zheng
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  3. Lianxi Ma
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Corresponding author

Correspondence to Yanhai Lin.

Additional information

Project supported by the Scientific Research Funds of Huaqiao University (No. 14BS310) and the National Natural Science Foundation of China (Nos. 51276014 and 51476191)

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Lin, Y., Zheng, L. & Ma, L. Heat transfer characteristics of thin power-law liquid films over horizontal stretching sheet with internal heating and variable thermal coefficient. Appl. Math. Mech.-Engl. Ed. 37, 1587–1596 (2016). https://doi.org/10.1007/s10483-016-2141-8

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  • DOI: https://doi.org/10.1007/s10483-016-2141-8

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Chinese Library Classification

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